Related papers: Cascade replication of dissipative solitons
Dissipative vortices are stable two-dimensional localized structures existing due to balance between gain and loss in nonlinear systems far from equilibrium. Being resistant to the dispersion and nonlinear distortions they are considered as…
The effect of an externally applied force upon dynamics of dissipative solitons is analyzed in the framework of the one-dimensional cubic-quintic complex Ginzburg-Landau equation supplemented by a linear potential term. The potential…
The influence of an externally applied magnetic field upon classic cubic quintic dissipative solitons is investigated using both exact simulations and a Lagrangian technique. The basic approach is to use a spatially inhomogeneous magnetic…
We derive the complex Ginzburg-Landau equation for the dynamical self-diffraction of optical waves in a nonlinear cavity. The case of the reflection geometry of wave interaction as well as a medium that possesses the cubic nonlinearity…
We analyze the dynamics of dissipative solitons in silicon on insulator waveguides embedded in a gain medium. The optical propagation is modeled through a cubic Ginzburg-Landau equation for the field envelope coupled with an ordinary…
In this chapter we review recent results concerning localized and extended dissipative solutions of the discrete complex Ginzburg-Landau equation. In particular, we discuss discrete diffraction effects arising both from linear and nonlinear…
We study in detail the scattering of light on a soliton propagating in a waveguide which has been proposed as an experimental system in which one could observe the analogue Hawking effect. When not applying the rotating wave approximation,…
The time-dependent Ginzburg-Landau approach is used to investigate nonlinear response of a strongly type-II superconductor. The dissipation takes a form of the flux flow which is quantitatively studied beyond linear response. Thermal…
We use the cubic complex Ginzburg-Landau equation coupled to a dissipative linear equation as a model of lasers with an external frequency-selective feedback. It is known that the feedback can stabilize the one-dimensional (1D)…
Intermolecular forces are modeled by means of a modified Lennard-Jones potential, introducing a distance of minimum approach, and the effect of intermolecular interactions is accounted for with a self consistent field of the Vlasov type. A…
We consider the process of light scattering by optical solitons in a planar waveguide with homogeneous and inhomogeneous refractive index core. We observe resonant reflection (Fano resonances) as well as resonant transmission of light by…
General nonlinear and nonparaxial dissipative complex Helmholtz equations for magnetic and electric fields propagating in negative refractive index materials (NIMs) are derived ab initio from Maxwell equations. In order to describe…
We propose and theoretically investigate a model to realize cascaded optical nonlinearity with few atoms and photons in one-dimension (1D). The optical nonlinearity in our system is mediated by resonant interactions of photons with…
Approximate analytical chirped solitary pulse (chirped dissipative soliton) solutions of the one-dimensional complex cubic-quintic nonlinear Ginzburg-Landau equation are obtained. These solutions are stable and highly-accurate under…
We discuss the Lorentz model for dispersion and absorption of radiation in dilute, linear and isotropic materials. Initially, with the purpose of making the paper as self-contained as possible, we reproduce the usual calculations concerning…
We consider nonlinear effects in scattering of light by a periodic structure supporting optical bound states in the continuum. In the spectral vicinity of the bound states the scattered electromagnetic field is resonantly enhanced…
Propagation characteristics of the chirped dissipative solitary waves are investigated within the framework of higher order complex cubic quintic Ginzburg Landau equation. Potentially rich set of exact chirped dissipative pulses, such as,…
Non-linear electrodynamic models are re-assessed in this paper to pursue an investigation of the kinematics of the Compton effect in a magnetic background. Before considering specific models, we start off by presenting a general non-linear…
We study the propagation of few-cycle pulses in two-component medium consisting of nonlinear amplifying and absorbing two-level centers embedded into a linear and conductive host material. First we present a linear theory of propagation of…
We demonstrate the occurrence of anomalous diffusion of dissipative solitons in a `simple' and deterministic prototype model: the cubic-quintic complex Ginzburg-Landau equation in two spatial dimensions. The main features of their dynamics,…